*TL;DR version: No.*

This is another entry to file under "notes for undergrads" and/or "explaining things to your neighbor". A very common question I get about growth is: how does growth occur if there is not any "more money" in the economy. Another common question I get is: how is it economic growth if spending on one product just replaces spending on another?

These questions come, I think, from continued confusion about (a) nominal versus real GDP, (b) nominal GDP versus the stock of money, and (c) absolute versus relative prices. In short, things an economist might call money illusion. In the defense of students and my neighbors, it isn't terribly easy to think in relative prices and real terms when every single transaction you undertake involves absolute dollars.

Let's start with an economy that produces exactly 10 cans of Budweiser, and nothing else, in a year. They each sell for \$1, meaning that nominal GDP in this economy is \$10 for the year. What is real GDP? Well, we already really know the answer - it's 10 cans of Budweiser.

Real GDP is measured in "real units". That's obvious in this example, because the real units are obvious - cans of Bud. To do this more formally, we find real GDP by dividing nominal GDP by a price index. In this case, the price index is easy to figure out. It's \$1 per can of Bud. So real GDP is \$10/\$1 per can of Bud = 10 cans of Bud.

One confusion with real GDP is that the BEA and economic textbooks insist on talking about it in terms of dollars. That is because the price index they use is not something like "\$1 per can", but is something like "\$1.37 per \$1 of output in 2005". So real GDP is $10/$1.37 per 2005 dollar = 7.3 units of 2005 dollars, which would be reported as "\$7.3 (2005 dollars)." But despite being reported in terms of dollars, real GDP has nothing to do with money.

I sometimes think that we should save our effort at coming up with good price indices, and just use something like the price of a can of Bud, or a pair of Levi 501 jeans, as the price deflator in national accounts. Because then real GDP would be reported in real, tangible units, and would save us from confusing it with a nominal number. For example, if the price of a can of Bud was \$0.50, then real GDP in the US for 2014 would be \$17,615 billion/ $0.50 per can on Bud = 35,230 cans of Bud. Nominal GDP through Q3 2015 is \$18,060, so that's real GDP of 36,120 cans of Bud, a 2.5% increase in real GDP from 2014. I'm laboring this point because when it comes to explaining how growth works, this confusion between nominal and real concepts becomes a problem.

Let's go back to our simple 10-can economy, with a price per can of \$1, and see how growth works.

**Growth through expanding production of existing products:** This is the easiest to explain. Something happens at Anheuser-Busch that lets them produce even more cans of Bud with their given inputs. Perhaps they water it down even more than it already is. Whatever the reason, the economy produces 12 cans of Bud this year. We *know* that real GDP went up, from 10 cans to 12 cans.

But let's walk through how to do this calculation using nominal GDP and a price index. Think of two possibilities

**Nominal GDP stays constant.**That is, nominal GDP is still \$10. Then it*must*be that the price of a Bud fell to \$0.83. The supply curve of Bud shifted out, and hence the quantity of Bud went up and the price of Bud went down. Real GDP is \$10/\$0.83 per can = 12 cans of Bud. For the given flow of money through the economy -*which does not have any necessary relationship to real GDP*- the price of a can of Bud must adjust to make supply equal demand.**The price of Bud stays constant.**Let each can still be \$1. The it*must*be that nominal GDP is \$12, and real GDP is \$12/\$1 per can = 12 cans of Bud. Here, the supply curve of Bud has shifted out, but apparently the demand curve shifted out as well, leaving the price unchanged and the quantity higher. Why would this happen? Who knows, and who cares. It's possible. For a given flow of money through the economy, the price of a can of Bud must adjust to make supply equal to demand.

Note that it is irrelevant whether nominal GDP goes up or stays constant (it could even fall). Whether nominal GDP rises or not is *completely irrelevant* to whether real GDP goes up. If we could observe the real quantity of cans consumed, we wouldn't need nominal GDP at all. But we don't actually observe the number of cans of Bud consumed. All we observe is nominal GDP and the price of a can of Bud. So when the BEA reports a nominal GDP of \$10, and a price of \$0.83 per can, we divide and infer that real GDP is 12 cans of Bud.

If your question now is where people get the "extra money" to afford 12 cans of Bud when their price stays at \$1, take a moment to meditate on the equation $MV = PY$. We'll come back to that in a few paragraphs.

**Growth through addition of new products:** This one will stretch the mind a little more, but the same principles are going to hold. Rather than Bud watering down their beer even further, we're going to introduce a new beer into the market. Someone - and God bless them - invents Real Ale Coffee Porter. In response, people with functioning taste buds buy 5 cans of Coffee Porter, and everyone else still buys 5 cans of Bud. So we've still only got 10 cans of beer being sold. Is this economic growth, meaning that real GDP is higher?

It depends on relative prices. If those cans of Coffee Porter are more expensive than cans of Bud, then this represents real economic growth. Why? Because if the relative price of Coffee Porter is higher than that of Bud, then the relative marginal utility of Coffee Porter is higher than that of Bud. Assuming that utility for both has typical properties (declining MU), then we know the MU of the 5th can of Bud is higher than the 10th can. And since Coffee Porter has a higher MU than that, it follows that we are better off in utility terms. More intuitively, if we *weren't* better off, then why were we willing to substitute away from Bud even though Coffee Porter costs more?

Which suggests that if Coffee Porter and Bud sold for the same amount, then we aren't any better off. In this case it's a perfect substitute, and the choice of 5 of each is just random. It's the difference in relative prices that a new product introduces that defines it's contribution of real growth.

So eocnomic growth is just about things getting more expensive? No. Note that I didn't say anything about the absolute price of Bud or Coffee Porter - because that is irrelevant for real GDP. So long as Coffee Porter is more expensive *than Bud*, we've experienced real growth. That holds if Porter costs \$2 to Bud's \$1, or \$20 to Bud's \$10, or \$0.02 to Bud's \$0.01.

Once we've established that there is a relative price difference, then the same questions about nominal GDP from before come up. Let's say that we observe that Coffee Porter costs twice as much as Bud. How do we calculate real GDP?

**Nominal GDP stays constant.**It must be that Bud costs \$0.67, and the porter is \$1.33, so nominal GDP is \$10 (multiply it out and you can see it). What is real GDP in this case? Sticking with our standard of using the price of Bud, real GDP is \$10/\$0.67 per can of Bud = 15 cans of Bud. It is*as if*our economy produced 15 cans of Bud, where before it only produced 10. There is real GDP growth due to the introduction of Coffee Porter - even though all Coffee Porter does is replace consumption of Bud and total beer drinking stays constant at 10 cans.**The price of Bud stays constant.**If Bud still costs \$1, then the porter is \$2. So nominal GDP is \$15 (again, just multiply it out). What is real GDP? \$15/\$1 per can of Bud = 15 cans of Bud. Real GDP has gone up. It is irrelevant what the nominal price of Bud is, we observe real GDP growth because the introduction of Coffee Porter introduced a relative price difference.

Notice that if all the BEA reports to me is nominal GDP and the price of Bud, I can infer real GDP regardless of what exactly happens. Our "Bud-based" measure of real GDP goes up to 15. I don't actually have to observe the number of cans purchased.

This example of adding a new product brings up one issue with price indices, which is product replacement. If - as would be logical if people tasted them - the introduction of Coffee Porter completely eliminated Bud from the market, then we cannot calculate real GDP. There will be no price of Bud to divide nominal GDP by. And we can't just use the price of Coffee Porter, because yesterday all we had was Bud, and there was no price for Coffee Porter. One of the reasons we use more sophisticated price indices (that combine the price of Bud and Coffee Porter in some way) is so that we always have a price index to use. But that sophisticated price index, by putting things in "2005 dollars" or something like that, creates confusion between real GDP and nominal GDP. Always think of real GDP as being "cans of Bud", rather than in dollar terms.

Now, If you are still wondering where people get the "extra money" to buy the Coffee Porter in this example, then the next section is for you.

**Where does the extra money come from?** Nowhere. There is no extra money. Nominal GDP is *not* a measure of "how much money we have". Nominal GDP is the flow of dollars through the economy. The stock of money is, well, a stock. In all the examples above, what is the stock of money? You can't answer that question, because I never said anything about it.

Let's say that this economy has a stock of 4 one-dollar bills. Here's the transactions flow in this economy in the initial stage, with only 10 can of Bud consumed:

- Person A starts with the \$4. (Nominal GDP is zero)
- Person A buys 4 Buds for \$4 from person B. (Nominal GDP is \$4)
- Person B buys 4 Buds for \$4 from person C. (Nominal GDP is now \$8)
- Person C buys 2 Buds for \$2 from person D. (Nominal GDP is now \$10)
- Person D ends up with \$2 and person C with $2. (Final nominal GDP is \$10)

Then next period we start again, only now C and D hold the money stock. The money stock is always \$4, and it gets turned over and over, resulting in \$10 of nominal transactions, or GDP. (No, it doesn't matter that the circle isn't closed here, with different people ending up with the actual dollars.) Real GDP is 10 cans of Bud.

If we have the case where Coffee Porter gets introduced, things look like this.

- Person A starts with the \$4. (Nominal GDP is zero)
- Person A buys 2 Porters for \$4 from person B. (Nominal GDP is \$4)
- Person B buys 4 Buds for \$4 from person C. (Nominal GDP is now \$8)
- Person C buys 2 Porters for \$4 from person D. (Nominal GDP is now \$12)
- Person D buys 1 Bud for \$1 and 1 porter for \$2 from person E. (Nominal GDP is now \$15)
- Person D ends up with \$1 and person E with \$3. (Final nominal GDP is \$15)

No "new money" is necessary. Real GDP is 15 cans of Bud. The same \$4 gets recycled over and over again, this time used to purchase both Buds and Porters. Different people end up with money stock at the end. We could easily write out an example where the growth occurred because of just an increase in the number of Buds. And if you prefer that nominal GDP not increase, you can easily go back and work out the same set of transactions, lower the absolute prices, and get nominal GDP to come out to exactly \$10. And yes, I made up these examples. But I just need to show you that it is possible to get economic growth even though there is no new money in the economy.

Economic growth occurs either because we produce more of existing things, or because we introduce new things that that are more valuable than the old things we produced - which shows up in *relative* price differences. The level of absolute prices is irrelevant. The level of nominal spending is irrelevant. The stock of money is irrelevant.

For any modern economy, it is effectively impossible for there to be "not enough money" to let growth occur. The economy as a whole can always turn over the money stock faster to allow for the extra transactions if necessary. Whether that turnover involves *you*, and means that *you* can afford to buy some Coffee Porter, is a different question, and involves your own productivity and/or ownership of a Bud- or Coffee Porter-producing machine.